THE ORBITS OF THE EIGHT PRINCIPAL PLANETS. >9 



For the root </ 4 =0".6 166859, we get, 



3.357579 1.360360 /r 58981.24 



Whence /3 4 =67 56' 38".9 ; log. ^/ r =95.8033000. 



N 4 =+0.000007695; JV/ r =+0.000063577 ; 



A7 =+0.00001 170; NJ =+0.000071706; 



^"=+0.000013569 ; N t n =+0.00155781 ; 



JV'"=+0.000021904 ; JV 4 "'=+0.01003935. 



For the root <7 6 =2". 727684, we get, 



0.6476505 r 0.1746351 345.2619 



_ . r . _ 



X& ~ 10' ' ^ 5 ~~ 10 ' 2fi 



Whence &=105 5' 26".0 ; log. JV 5 /r ==97.2884328. 



N, =+0.00056110; N 6 17 =+0.00194282; 



#,' =-{-0.00055299; N* =+0.00176878; 



JV 6 " =+0.00058126 ; N & rl =+0.02973089 ; 



JV 5 "'=+0.00077406 ; JV 6 F// = 0.00291023. 



For the root # 6 =3".7 16923, we get, 



_0.4583310 A7/r , 0.8566739 AT/r 22.51056 F2 



"~~ -"e 2 e ~~~ I -" 



Whence /2 6 =28 8' 50".4 ; log. NJ "=98.6350898. 



N 6 =+0.0238845; N e ir =+0.04316083 ; 



N,' =+0.0163985 ; N 6 V =+0.03410240 ; 



JV 6 " =+0.0162413 ; N e VI = 0.04484797 ; 



iV 6 '"=+0.0187424 ; ^ 6 "'=+0.00141946. 



For the root # 7 ,=22".460985, we get, 



L009476 v f , 0.7872105 ^ r , Y , 81.85731 Affr2 



^ TTMO " ' y^ + inio -"T > z i + imo "! 



Whence ^ r =307 56' 52".2; log. JV/ r =98.1941978. 



N r =0.0001043 ; N, IV =+0.01563860; 



Nj' =+0.0004095 ; N, r =0.04835037 ; 



N,"= 0.0024158 ; N," =+0.00180575 ; 



JV/"= 0.0152719 ; N 7 T "= +0.000136497 



30. The assumed mass of the earth was obtained on the hypothesis that the 

 mean equatorial parallax of the sun is only 8".50. Recent investigations indicate 

 that the sun's parallax is greater by at least one- thirtieth part. Consequently the 

 assumed mass of the earth is too small by its one-ninth or one-tenth part; and on 

 account of the importance of this element in most astronomical theories, we shall 

 here give another determination of the constants corresponding to an increment of 

 V to the earth's mass. This new determination will be useful as an indication to 



